A Review of Techniques for Implementing Elliptic Curve Point Multiplication on Hardware

Arielle Verri Lucca,Valderi Leithardt,Marko Beko,Wemerson Parreira,Guilherme Mariano Sborz,Cesar Albenes Zeferino

doi:10.3390/jsan10010003

Abstract

Cryptography is considered indispensable among security measures applied to data concerning insecure means of transmission. Among various existent algorithms on asymmetric cryptography, we may cite Elliptic Curve Cryptography (ECC), which has been widely used due to its security level and reduced key sizes. When compared to Rivest, Shamir and Adleman (RSA), for example, ECC can maintain security levels with a shorter key. Elliptic Curve Point Multiplication (ECPM) is the main function in ECC, and is the component with the highest hardware cost. Lots of ECPM implementations have been applied on hardware targeting the acceleration of its calculus. This article presents a systematic review of literature on ECPM implementations on both Field-Programmable Gate Array (FPGA) and Application-Specific Integrated Circuit (ASIC). The obtained results show which methods and technologies have been used to implement ECPM on hardware and present some findings of the choices available to the hardware designers.

Highlights

The rapid development and widespread application of information technology have deeply affected the entire economy and society
One approach to provide public-key cryptography relies on the use of Elliptic Curve Cryptography (ECC), which is based on the algebraic structure of elliptic curves over finite fields
ECC was proposed by Neal Koblitz [1] and Victor Miller [2], and requires smaller keys to obtain the same security level when compared to other algorithms

Summary

Introduction

The rapid development and widespread application of information technology have deeply affected the entire economy and society. Shamir and Adleman (RSA) key, ECC will need a 256-bit key to ensure the same security level [3]. Since the code must be compact, designers must select the functions properly to provide efficiency without compromising the primary function. It is well-known that selecting the best cryptographic scheme and algorithms has a preponderant role in the design task. According to Loi and Ko [21], ECC needs smaller keys than RSA to provide the same level of security. This aspect is why we defined ECC as our object of study. While smaller keys do not guarantee smaller code, the advantages of ECC rely on the security aspect

Methods

Results

Conclusion